There's decent empirical evidence of an effect.

It's not a huge surprise when you think about it - therapy works because of helping people change how they think.

The reason it's often dismissed by skeptics is because it's often surrounded by a lot of religious woo and other nonsense so people often dismiss the entire thing.

I have a pet hypothesis that it can make anxiety worse if you're not careful due to Hypervigilance (https://en.wikipedia.org/wiki/Hypervigilance) - anxious people tend to have issues with ruminating and paying too much introspective attention to their bodies already. Most meditation rhetoric appears to be targeted to people who never introspect. Getting control over ruminating thoughts is helpful, but I've found mindfulness to be a mixed bag personally.